Add a Matrix Diagonalization node (
) under
Definitions>Variable Utilities (if
Group by Type is active; otherwise, directly under
Definitions) to define variables representing the diagonalization of a symmetric 3-by-3 input matrix. You add it by right-clicking the
Definitions node and choosing
Variable Utilities>Matrix Diagonalization or by right-clicking the
Variable Utilities node and choosing
Matrix Diagonalization.
You can define a Label for the node, and a namespace for variables using the
Name field. For the
Geometric Entity Selection, see
About Selecting Geometric Entities.
In addition, the Settings window for a
Matrix Diagonalization node contains the following sections:
Select the Compute exponential check box to compute also the matrix
eT, where
T is the input matrix.
Select the Ignore Jacobian contributions check box (selected by default) to ignore any solution dependencies during the solution process.
The principal values become available as variables <name>.e<i>, where
<name> is the namespace set in the
Name field, and
<i> is the principal component index, ordered from largest to smallest absolute value. Components of the corresponding principal vectors are called
<name>.e<i><j>, where
<j> are integer indices. If
Compute exponential was selected, the result can be evaluated as a list of variables with names
<name>.expT<i><j>. The input matrix with names
<name>.T<i><j>, as well as its determinant
<name>.detT are also made available. Note that the determinant is not computed for matrices of size 4-by-4 or larger; if required, use a
Matrix Decomposition node instead.
You can use individual components where variable expressions are allowed, but also evaluate complete vectors and matrices at once using a matrix evaluation node under Derived Values. For example, to evaluate the first principal vector, select
matdiag1.e1_vec under
Model>Component 1>Definitions>Matrix Diagonalization 1>Principal vector 1 if the node has been defined as
Matrix Diagonalization 1 with the name
matdiag1 in
Component 1.